Ground-state density-functional theory (DFT) and time-dependent density-functional theory (TDDFT) are popular electronic structure methods among chemists, thanks to their balance between accuracy and computational cost. DFT methods achieve this balance through a mapping from the real world system with interacting electrons to a fictitious non-interacting Kohn-Sham (KS) system with the same electronic density, allowing one to represent the properties of the real system as functionals of the density. The connections between the real world and the non-interacting world are unclear in many aspects, and exact physical constraints for these connections must be derived to make DFT and TDDFT work better.
This dissertation contains two closely related parts studying the connections between the real systems and the KS systems. In the first part, I study the oscillator strength at the ionization threshold of helium, and I reach the conclusion that the KS oscillator strength at the ionization threshold is not exact, despite the exactness of the position of the ionization threshold. I observe that the high-frequency behavior of the oscillator strength of all atoms decays as ω−7/2, implying non-time-Taylor-expandability in the time-domain. This observation leads to the second part of the dissertation, in which I demonstrate that the time-dependent wavefunctions are not time-Taylor-expandable whenever the initial wavefunction has derivative discontinuities at any order, due to specific time-non-analyticities occurring at the initial time. The analysis of these time-non-analyticities is given in this dissertation, and I propose a method of obtaining the correct short-time behavior of such systems.
|Commitee:||Mandelshtam, Vladimir, Martens, Craig|
|School:||University of California, Irvine|
|Department:||Chemistry - Ph.D.|
|School Location:||United States -- California|
|Source:||DAI-B 72/11, Dissertation Abstracts International|
|Keywords:||Kohn-Sham system, Oscillator strength, Short-time behavior, Time-dependent density-functional theory, Time-non-analyticity|
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